The standard collective quantization treatment of the strangeness content of the nucleon in chiral soliton models, for instance Skyrme-type models, is shown to be inconsistent with the semi-classical expansion on which the treatment is based. The strangeness content vanishes at leading order in the semi-classical expansion. Collective quantization correctly describes some contributions to the strangeness content at the first non-vanishing order in the expansion, but neglects others at the same order-namely, those associated with continuum modes. Moreover, there are fundamental difficulties in computing at a constant order in the expansion due to the non-renormalizable nature of chiral soliton models. Moreover, there are fundamental difficulties in computing at a constant order in the expansion due to the non-renormalizable nature of chiral soliton models and the absence of any viable power counting scheme. We show that the continuum mode contribution to the strangeness diverges, and as a result the computation of the strangeness content at leading non-vanishing order is not a well-posed mathematical problem in these models.
|Original language||English (US)|
|Number of pages||5|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - Jul 19 2007|
Bibliographical noteFunding Information:
This work is supported by the US Department of Energy under grant number DE-FG02-93ER-40762. We are grateful to David Kaplan, Igor Klebanov, and Victor Kopeliovich for helpful discussions.